European Patent Application EP 1 323 497 A3 discloses a machine for the production of optically active surfaces with an electronically speed-controlled workpiece receptacle that can be rotated around a C-axis and that has a tool carriage which, relative to the C-axis, can move in the radial direction of an X-axis and in the axial direction of a Z-axis. Here, for the axial feed movement, there is a linear motor and for the X-, Z- and C-axes, there is a control processor that controls the position of the Z-axis, the position of the X-axis as well as the rotation of the C-axis. In addition, the axes are arranged essentially vertically or else they span a vertical machining plane. In addition to the axis of translation x, the tool receptacle also has the oscillating axis z.